We show that, in the saturation/Color Glass Condensate framework, odd azimuthal harmonics of the two-gluon correlation function with a long-range separation in rapidity are generated by the higher-order saturation corrections in the interactions with the projectile and the target. At the very least, the odd harmonics require three scatterings in the projectile and three scatterings in the target. We derive the leading-order expression for the two-gluon production cross section which generates odd harmonics: the expression includes all-order interactions with the target and three interactions with the projectile. Here, we evaluate the obtained expression both analytically and numerically, confirming that themore » odd-harmonics contribution to the two-gluon production in the saturation framework is non-zero.« less

A demore » tailed study of multiparticle azimuthal correlations is presented using pp data at $$\sqrt{s}$$=5.02 and 13 TeV, and p+Pb data at s NN =5.02 TeV, recorded with the ATLAS detector at the CERN Large Hadron Collider. The azimuthal correlations are probed using four-particle cumulants c n{4} and flow coefficients v n{4}=(-c n{4}) 1/4 for n=2 and 3, with the goal of extracting long-range multiparticle azimuthal correlation signals and suppressing the short-range correlations. The values of c n{4} are obtained as a function of the average number of charged particles per event, N ch, using the recently proposed two-subevent and three-subevent cumulant methods, and compared with results obtained with the standard cumulant method. The standard method is found to be strongly biased by short-range correlations, which originate mostly from jets with a positive contribution to cn{4}. The three-subevent method, on the other hand, is found to be least sensitive to short-range correlations. The three-subevent method gives a negative c 2{4}, and therefore a well-defined v 2{4}, nearly independent of N ch, which implies that the long-range multiparticle azimuthal correlations persist to events with low multiplicity. Furthermore, v 2{4} is found to be smaller than the v 2{2} measured using the two-particle correlation method, as expected for long-range collective behavior. Finally, the measured values of v 2{4} and v 2{2} are used to estimate the number of sources relevant for the initial eccentricity in the collision geometry. Finally, the results based on the subevent cumulant technique provide direct evidence, in small collision systems, for a long-range collectivity involving many particles distributed across a broad rapidity interval.« less